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Role of the Poisson Distribution

The Poisson distribution is used in practice in a wide variety of problems where there are infrequently occurring events with respect to time, area, volume or similar units. Some practical situations in which Poisson distribution can be used are given below:

(1) it is used in quality control statistics to count the number of defects of an item,

(2) in biology to count the number of bacteria,

(3) in physics to count the number of particles emitted from a radioactive substance,

(4) in insurance problem to count the number of casualties,

(5) in waiting-time problems to count the number of incoming telephone calls or incoming customers,

(6) number of traffic arrivals such as trucks at terminals, aeroplanes at airports, ships at docks, and so forth.

(7) in determining the number of deaths in a district in a given period, say, a year, by a rare disease.

(8) the number of typographical errors per page in typed material, number of death as a result of road accidents, etc.,

(9) in problems dealing with the inspection of manufactured products with the probability that any one piece is defective is very small and lots are very large,

(10) to model the distribution of the number of persons joining a queue (a line) to receive a service or purchases of a product.

In general, the Poisson distribution explains the behavior of these discrete variates where the probability of occurrence of the event is small and the total number of possible cases is sufficiently large.

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